25 October 2014

Another Difficult SP for Black

The post from a few weeks ago, A Half-Tempo Advantage, reminded me that I had one game left from last year's Proof of Concept with HarryO. After examining A Difficult SP for Black (SP868 QBBRKRNN), we looked at its cousin (SP864 BBQRKRNN) which is largely the same position except that a Queen and a Bishop are switched at the start.


White's first move is again 1.Ng3, threatening 2.Nf5. To defend against the attack on g7, Black must make a positional concession already on the first move. To see how HarryO and I handled it -- I had Black -- you can find our moves on HarryO's blog as comments to Non-Random Chess960 Trial Game 9: SP864 after 4)...e6.

I also flagged the position on a couple of chess960 forums. I'll discuss the feedback in my next post.

18 October 2014

Updated Database of SPs (2014-10)

It's been a year since I last Updated the Database of SPs (2013-10), so I added the posts written since then. These are all posts discussing specific positions and my database is to keep track of them by SP.

A couple of these posts discussed multiple positions -- Nakamura's 1.g4/b4 and Nakamura's 1.h4/a4 -- and I added a database entry for each position discussed. One of these positions was already in the database -- SP931 BRKRNQNB -- so that database entry now points to both posts where it was discussed. Ditto for SP190 - NRNKRBBQ.

As long as I was doing blog maintenance, I decided to restructure parts of Chess960 1-2-3 : Index to Blog Posts. I could have also added all blog posts since A New Page, a TOC, and a Logo (June 2014), but I'll leave that for another time.

11 October 2014

A Half-Tempo Advantage

Not too long ago, my Blogspot.com stats flagged an incoming link from the Arimaa.com forum, Re: Measure stereotyped openings. The link was to a post from two years ago, Waving a Yellow Flag, where I listed a number of chess960 start positions that, according to CCRL experiments, seemed to produce superior results for White. The Arimaa.com poster concluded,
Under the assumption that every chess960 position has exactly the same first-move advantage, by natural variation I get results just as extreme as the ones our blogger has compiled. So perhaps some positions have just been lucky for White so far, and others unlucky, with no inherent bias. At a minimum, if these are the most conclusive stats available, we have to say there is so far no statistical evidence that some positions favor White more than others.

In other words, the CCRL results match the distribution one would expect from the number of games in the CCRL sample, assuming a 55%-45% theoretical advantage for White. I asked Ichabod, the chess960 expert and professional statistician last seen on this blog in A Better Pawn Method, if he agreed with the post on the Arimaa forum and he confirmed its methodology. Then I asked him, 'How big would the samples have to be to reduce the extremes to their theoretical minimum?' He answered,

It's not a question of theoretical minimum. The question is, are the results you are seeing more extreme than you would expect with random chance? If you aren't, then there isn't statistical evidence of an effect.

To clarify, you need to think about how much of an advantage you want to detect. What you're seeing is that at your current sample size you can't detect an advantage of 12% because of the random noise. What advantage do you want to detect? 5%? 1%? From that you could back calculate a necessary sample size from the multinomial win/loss/draw distribution.

Last year, on my main blog, I posted a series on Practical Evaluation, where I learned that the value of the first move in traditional chess is a half-tempo, which is worth 0.2 times the value of a Pawn. In the last post in the series, I learned that A Pawn Equals 200 Rating Points, which gives White a theoretical advantage of 56%-44% based on the half-tempo. This is very close to the observed advantage for White over millions of games.

Given that all of the start positions in chess960 confer a half-tempo advantage on White, does that mean White always has an advantage of 56%-44%? Or perhaps the half-tempo advantage isn't equivalent to 0.2 times a Pawn for all 960 start positions. I suspect the latter is true, but how will we ever find out, given that we need so many games with each start position to provide a valid sample.

I asked Ichabod, 'How many games would I have to play in another start position to know that the new W%-B% is significantly different?' He answered,

Here we get into the issue of the two different kinds of significance: statistical significance and practical significance. Statistical significance is going to determine what sample size you need to detect a given difference. Practical significance is going to determine what difference you want to detect. Say we had a bazillion games for each position, and we could show that in some positions White had an advantage of 0.000001 pawns. No one would care. We would have statistical significance but we wouldn't have practical significance.

On the other hand, let's say in certain positions we could show with statistical significance that white had a full Pawn advantage. Then people would care, and would think that position is flawed. We would have both practical and statistical significance. Now, somewhere between 0.000001 pawns and a full Pawn is a minimum advantage that would be considered a practically significant difference between the standard position and a given chess960 position.

Determining that minimum advantage is not a statistics question, it's a chess question. That is, you have to determine what fraction of a Pawn advantage is a practically significant advantage.

Here's an idea for killing a large amount of time: Run an engine (any chess960-enabled engine) on all 960 start positions (SPs). Record the value of the top-10 first moves for each SP. Analyze the results. Can any information be derived from the observed value of the first moves?

04 October 2014

Nakamura's 1.h4/a4

First I took a bird's-eye look at Nakamura's Chess960 Openings, then looked at four examples of Nakamura's 1.g4/b4. Now I'll look at some examples of 1.h4 and 1.a4.

In the traditional chess start position, the move 1.b4 has its dedicated adherents, while 1.g4 is considered dubious, despite a small number of fans. The moves 1.h4 and 1.a4 are both considered to be even worse than 1.g4. In chess960, the boundaries between good first moves and poor first moves shift depending on the start position. GM Nakamura opened with 1.h4 or 1.a4 in three games recorded on ICC:-

  • SP544 BBRNKNQR: 2002.10.25, Smallville - JelenaDokic
  • SP703 RQKNNRBB: 2009.07.27, Smallville - OfficeMan
  • SP501 RQBBNKNR: 2004.08.10, Smallville - McShane

At first I wasn't going to consider the game played in 2002, because it is Nakamura's earliest recorded chess960 ICC game. The choice of 1.h4 might have been a youthful indiscretion played for no particular reason. Then I looked at the game, shown in the top diagram below. With the two Bishops aimed at the opponent's h-side and the Queen-Rook sitting behind the g-/h-Pawns, the move 1.h4 launches an immediate attack. White's aggressive opening strategy is apparent already on the first move.

The two bottom diagrams are from the later games. In SP703, the pieces on the a-/b-/g-/h-files mirror the same pieces in SP544. The two positions would be twins if the King and a Knight were switched. Following the logic in SP544, White could have played 1.a4, but 1.h4 was played again, apparently to develop the Black-squared Bishop via h2.

In SP501, the Rook-Queen pair is again in the corner, this time without the dynamics in the opposite corner. White played 1.a4, followed by 2.Ra3 and 3.b4 on the next two moves. For his initial moves, Black pushed Pawns in the center and ultimately won. It was the only game of the three where Nakamura did not prevail.

What can be learned from these three examples? First, that a game's strategy starts on the very first move. Second, that the strategy should pay some attention to classical opening principles. Third, that White can use the initial tempo to try something offbeat. But we already knew all that from traditional chess, didn't we.